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P(tails | previous 19 flips were heads) =P(tails I previous 19 flips being heads)/P(previous 19 flips being heads) Since the events are independent (one coin flip does not effect the result of another coin flip), the P(tails I previous 19 flips were heads)=P(tails)*P(previous 19 flips were heads). Thus, the P(previous 19 flips were heads) cancels out, giving us P(tails | previous 19 flips were heads)=P(tails)=1/2. Thinking an outcome is more likely to happen is a common fallacy. It may be highly unlikely to see 20 heads flipped in a row, but the hard part has already been accomplished (the 19 heads being flipped in a row).